Free Grade 3 Working with Adding Vectors Quizzes
Free Grade 3 quizzes for Working with Adding Vectors: 12 real questions with a full answer key and worked solutions. A vector has size and direction. Add vectors component by component; multiply by a number to scale. Magnitude = √(x² + y²).
Free
Higher
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with adding vectors
Explain working with adding vectors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with adding vectors
Calculate working with adding vectors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with adding vectors
Compare working with adding vectors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with adding vectors
Justify working with adding vectors accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Working with Adding Vectors works
A vector has size and direction. Add vectors component by component; multiply by a number to scale. Magnitude = √(x² + y²).
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.a = (-4, -3), b = (6, -5). Find a + 3b.[1]
- 2.a = (-2, -4), b = (2, -6). Find a + 2b.[1]
- 3.a = (-1, 0), b = (-1, -2). Find a + 2b.[1]
- 4.a = (-5, -4), b = (-2, 0). Find a + 2b.[1]
- 5.a = (-5, 6), b = (-3, -3). Find a + 2b.[2]
- 6.a = (6, 6), b = (-3, 6). Find a + 4b.[2]
- 7.a = (-1, -6), b = (-6, -2). Find a + 2b.[2]
- 8.a = (5, -2), b = (-3, -3). Find a + 2b.[2]
- 9.Find the magnitude of (0, -5) to 2 d.p.[3]
- 10.Find the magnitude of (3, 0) to 2 d.p.[3]
- 11.Find the magnitude of (-2, 2) to 2 d.p.[3]
- 12.Find the magnitude of (2, -4) to 2 d.p.[3]
Show answers and working
1. (14, -18)
3b = (18, -15). Add components: (-4 + 18, -3 + -15).
2. (2, -16)
2b = (4, -12). Add components: (-2 + 4, -4 + -12).
3. (-3, -4)
2b = (-2, -4). Add components: (-1 + -2, 0 + -4).
4. (-9, -4)
2b = (-4, 0). Add components: (-5 + -4, -4 + 0).
5. (-11, 0)
2b = (-6, -6). Add components: (-5 + -6, 6 + -6).
6. (-6, 30)
4b = (-12, 24). Add components: (6 + -12, 6 + 24).
7. (-13, -10)
2b = (-12, -4). Add components: (-1 + -12, -6 + -4).
8. (-1, -8)
2b = (-6, -6). Add components: (5 + -6, -2 + -6).
9. 5
|v| = √(x² + y²) = √(0 + 25). = 5.
10. 3
|v| = √(x² + y²) = √(9 + 0). = 3.
11. 2.83
|v| = √(x² + y²) = √(4 + 4). = 2.83.
12. 4.47
|v| = √(x² + y²) = √(4 + 16). = 4.47.
Worked examples
a = (6, 1), b = (3, -6). Find a + 4b.
- 4b = (12, -24).
- Add components: (6 + 12, 1 + -24).
- Answer: (18, -23)
a = (-1, 0), b = (-6, 4). Find a + 3b.
- 3b = (-18, 12).
- Add components: (-1 + -18, 0 + 12).
- Answer: (-19, 12)
Find the magnitude of (-1, -6) to 2 d.p.
- |v| = √(x² + y²) = √(1 + 36).
- = 6.08.
- Answer: 6.08
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Adds x of one vector to y of the other.
Correction: Add x with x, y with y.
Forgets that a negative component means the opposite direction.
Correction: Draw the vector to check.
Teacher tips
- · Draw vectors on squared paper end to end.
Parent tips
- · Give directions as '3 steps right, 2 steps up'.
Real-life applications
- · Navigation, forces in physics, game movement.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 Working with Adding Vectors quiz really free?
- Yes. Every quizzes on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Introducing Adding Vectors, Vector Notation. Each one has its own free lesson, worksheet and quiz.
- How is the quiz sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Working with Adding Vectors?
- Move on to Adding Vectors in Context, Vector Notation, Scalar Multiples, Magnitude of a Vector, which build directly on this idea.
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